Solve for $x$ and $y$ using elimination. ${-3x+2y = 6}$ ${2x-2y = -8}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-3x+2y = 6}\thinspace$ to find $y$ ${-3}{(2)}{ + 2y = 6}$ $-6+2y = 6$ $-6{+6} + 2y = 6{+6}$ $2y = 12$ $\dfrac{2y}{{2}} = \dfrac{12}{{2}}$ ${y = 6}$ You can also plug ${x = 2}$ into $\thinspace {2x-2y = -8}\thinspace$ and get the same answer for $y$ : ${2}{(2)}{ - 2y = -8}$ ${y = 6}$